See Theorem 3.7 of [1]} for the analysis. Recently, a deeper understanding of quasi-Newton methods for minimizing smooth and strongly convex objectives has been reported in [2]}, [3]}, [4]}, [5]}. These works enhanced the analysis based on Dennis-Moré condition by performing a local, non-asymptotic convergence analysis; and they provided explicit superlinear rates for different potential functions of quasi-Newton methods.
The non-asymptotic superlinear results are more informative than asymptotic superlinear results established via (REF ), i.e., \(\Vert _{t+1} - {^\star }\Vert /\Vert _t - {^\star }\Vert \rightarrow 0\)  as \(t\rightarrow \infty \) . However, those analyses highly rely on specific properties of quasi-Newton updates in the Broyden class, and they do not apply for general Hessian approximations (e.g., finite difference approximation).
